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Mathematical Problems in Engineering
Volume 2014, Article ID 260869, 9 pages
Research Article

A Two-Stage Algorithm for the Closed-Loop Location-Inventory Problem Model Considering Returns in E-Commerce

School of Information Management, Central China Normal University, Wuhan 430079, China

Received 27 March 2014; Revised 12 August 2014; Accepted 22 August 2014; Published 28 September 2014

Academic Editor: Albert Victoire

Copyright © 2014 Yanhui Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Facility location and inventory control are critical and highly related problems in the design of logistics system for e-commerce. Meanwhile, the return ratio in Internet sales was significantly higher than in the traditional business. Focusing on the existing problem in e-commerce logistics system, we formulate a closed-loop location-inventory problem model considering returned merchandise to minimize the total cost which is produced in both forward and reverse logistics networks. To solve this nonlinear mixed programming model, an effective two-stage heuristic algorithm named LRCAC is designed by combining Lagrangian relaxation with ant colony algorithm (AC). Results of numerical examples show that LRCAC outperforms ant colony algorithm (AC) on optimal solution and computing stability. The proposed model is able to help managers make the right decisions under e-commerce environment.